论直流电位场拟解析近似中的电位与电荷反射函数的物理意义

On the Physical Meaning of the Surface Potential and the Surface Charge Density Reflection Functionsin in the QuasiAnalytical Approximations of the D.C.Electrical Potential Field

为了避开由大型代数方程组数值求解所带来的问题,将电场反射张量的基本概念和拟解析近似的基本思想引入到了直流电位场的数值模拟中,定义了体电位反射函数、面电荷反射函数和面电位反射函数等3个辅助函数,并给出了其在一般条件下的拟解析近似解和在简单条件下(均匀或点电流源背景场、均匀导电柱体或球体)的分析解。简单的对比分析证明:面电荷反射函数是异常体表面上自由面电荷密度的函数;在简单条件下,这种函数关系转化成为比例关系;类似的结论对于简单条件下的面电位反射函数也成立;然而,在一般条件下难以建立面电位反射函数和自由面电荷密度之间的明确关系。

For avoiding the problems caused by solving large linear equation systems numerically,we introduce the basic concept of the electrical reflectivity tensor and the basic idea of the quasi-analytical approximation into D.C.electrical potential field,and define three auxiliary functions,namely the volume potential reflection function,the surface potential reflection function,and the surface charge density reflection function.Also,we give the quasi-analytical approximations to the reflection functions for general cases and the analytical solutions of the reflection function in simple situations,i.e.a uniform or a point current source background electrical field and uniform cylinders and spheres as the anomalous body.Simple comparison shows that the surface charge density reflection function is a function of the free surface charge density on the surface of the anomalous body under consideration.In simple situations described above,the function reduces into a simple proportional relationship.The same is true for the surface potential reflection function in simple cases.However,in general cases it is difficult to establish an explicit relationship between the surface reflection function and the free surface charge density.